In the Vienna ab initio simulation package (VASP5.4),^7-10) the gradient approximation (GCA) method proposed by Perdew, Burke, and Ernzerhof (PBE),¹¹⁾ as well as the Monkhorst-Pack method, was employed. The cut-off was set to be 500 eV, which is a general criterion, and the K-mesh appropriate for each structure was used.¹²⁾ In addition, the simulation was performed by adopting the Project Augmented Wave (PAW) pseudopotential,^13,14) which is generally used for each element. Structural relaxation was performed to enable the variation of the atomic positions, lattice parameters, and the values for symmetry. After completing the structural relaxation, the energy values were verified. The band structure as well as the density of state (DOS) were also examined to verify if the calculation was carried out normally.

The raw material reagents selected through the DFT calculations (Sr, Li₃N, AlN, and EuN) were weighed and mixed according to the stoichiometry. They were then pulverized to prepare samples in a glove box that included oxygen and moisture less than 2 ppm. Then, 0.3 g of each sample was put into a boron nitride (BN) (80 × 40 × 20 mm) container that has 18 holes with a diameter of 8.5 mm. Subsequently, the BN container was transported to a sealed tube-type heat treatment system to calcinate the samples in a nitrogen atmosphere (N₂:H₂ = 95:5) at 1000°C for four hours. Each of the calcinated samples was then pulverized to undergo X-ray diffraction (XRD) and photoluminescence (PL) analysis. The emission spectrum was measured at 460 nm excitation by using a house-built continuous-wave (CW) PL system equipped with a xenon lamp.

The reactant energy and the product energy were obtained by the DFT calculation, and the reaction energy was calculated as the difference between the two energy values. The calculation results are shown in Table 1. Calculation was performed to obtain the energy values of the raw material reagents that were used as reactants in the SLA report,⁶⁾ which were SrH₂, LiAlH₄, AlN, and N, as well as the energy values of their products, which were SrLiAl₃N₄ and NH₃. The calculated reaction energy was −0.2224 eV/atom. The SLA fluorescent substrate⁶⁾ was synthesized by a general solid-state synthetic method, as described in the introduction. For this purpose, the selected raw materials were mostly nitrides. The selected raw materials were Sr, Li₃N, AlN, and N. In the case of Sr, the Sr metal was selected because the nitride reagent, Sr₃N₂, was not available. The calculated reaction energy was −0.1827 eV/atom. Comparison of the two reaction energy values showed that the method reported by the SLA report was more stable. However, the method chosen in the present study was found to be more stable when compared with the reaction energy values of similar inorganic compounds reported by Ceder,¹⁵⁾ thereby indicating that the synthetic method may be feasible.

In addition, since various raw material reagents were selected in the present study, the reaction energy of the individual reactants was calculated. A striking fact from the calculations was that a big difference in the calculation value was found only between the calculations performed by setting the source of Al as a metal and the calculations performed by setting the source of Al as AlN, regardless of the calculation methods. The calculated reaction energy value was about 5 to 6 times lower in the calculation performed by setting the Al source to be Al metal than in the calculation performed by setting the Al source to be AlN. This result was consistent with the optimal synthesis conditions for a series of nitride fluorescent substrates that are commercially applied. For example, the CASN (CaAlSiN₃:Eu²⁺) nitride red fluorescent substrate is synthesized by using the AlSi alloy metal as a raw material. Another example is the LSN (La₃Si₆N₁₁:Ce³⁺) yellow fluorescent substrate that is synthesized by using the LaSi₂ alloy metal as a raw material. These examples show that the possibility of synthesis increases when the Al metal is used as the Al source.

However, the correlation between the reaction energy and the synthetic route roughly explained in the present article does not provide an absolute standard of value. In particular, the DFT calculations performed in the present study are based on the simple thermodynamic internal energy at the absolute temperature of zero (0) under the assumption that all materials are solid. Therefore, the values obtained from the calculations do not represent the actual situation at high temperature involving many gas phases. It should be noted that the entropy term representing the gas phases was completely neglected and the kinetic term may not be considered in the simple DFT calculations. Nevertheless, considering that the reaction energy values obtained from the simplified calculations of the present study are well matched with the situation of the actual experiment, the calculation results may be used to predict the optimal conditions for synthesizing fluorescent substrates.

Based on the calculation results, the synthesis was performed by the Method No. 2 shown in Table 1. An XRD analysis was performed to verify if the synthesis of the SLA fluorescent substrate was well carried out. The calcinated samples did not have a single phase SLA structure, but included a small amount of impurity. The impurity phase was AlN, which was consistent with the reaction energy calculation results that showed the reaction energy value increasing when the AlN source was used. Fig. 1 shows the XRD pattern and the Rietveld refinement results of the SLA fluorescent substrate. The sample had a triclinic system structure in the P-1 space group. The lattice parameters were a = 5.8461 (2) A, b = 7.4791 (4) A, c = 9.9199 (4) A, α = 83.598 (2)°, β = 76.766 (5)°, and γ = 79.519 (6)°. In addition, the lattice parameters of the impurity phase, AlN, were a = 3.1082 (1) A, and c = 4.9743 (5) A. The space group was also found to be P6₃mc. Besides the AlN impurity phase, some unidentified peaks that were extremely small and weak were also found. The atomic position table reported by the SLA report from Schnick et al.⁶⁾ was selected as the initial Rietveld model. The Rietveld refinement was performed by using the Fullprof package. In the process of the Rietveld refinement, such variables as scale factor, zero correction, background, half-width, lattice, atom position, and thermal were optimized through the refinement procedures. The blue line in Fig. 1, which represents the difference between the experimental value and the calculated value, is almost flat. Hence, the profile consistency coefficients were as good as Rp = 6.44, Rwp = 8.43, and Rexp = 7.89 with x² = 1.14, indicating that the calculated profile was well matched with the experimental values. Despite the presence of unidentified peaks of impurities that could not be considered in the Rietveld refinement procedures, the value of x² was unaffected. Fig. 2 shows the shape of the structure viewed from the [011] direction, as calculated by the VESTA software. The overall structure is that of a host lattice having a high-density and rigid framework with aligned edges of AlN₄ and LiN₄ tetrahedron (AlN: 1.87 to 2.00 A and LiN: 1.98 to 2.10 A). A vierer ring channel was obtained along the [011] direction. The negative charge of the [LiAl₃N₄]²⁻ framework net structure was offset by integrating the Sr²⁺ ion. The SLA fluorescent structure that has a highly symmetric hexahedron (8 N atoms Sr-N: 2.69 ~ 2.91 A) is very advantageous for narrow half-width light emitting as it has two different crystallographic Sr sites. The SrN₈ polyhedron is infinitely generated along the [011] direction as it is connected with a common plane, and the Sr-Sr distance is 3.27 A. In the eight coordinates, the ionic radius of Eu²⁺ was 1.25 A, which was almost equal to that of Sr²⁺ (1.26 A). Therefore, the Sr²⁺ site may be occupied by the Eu²⁺ ion.

Figure 3 shows the emission spectrum of the synthesized SLA fluorescent substrate and that of the CASN fluorescent substrate that is commercially used. The half-width is narrower in the emission spectrum of the synthesized SLA fluorescent substrate than in that of the CASN fluorescent substrate, which is consistent with the report by Schnick et al..⁶⁾ The red fluorescent substrate that has such a narrow half-width has advantages in the preparation of high-quality warm-white pc-LED (CRI > 90). According to the experimental design obtained from the reaction energy calculations, the synthesis resulted in a good SLA fluorescent substrate structure, as shown by the emission spectrum, despite the presence of the AlN impurity. The larger Stokes shift and the broader emission spectrum band observed in the Eu²⁺ fluorescent substrate has been generally correlated with the asymmetric dopant site geometry.¹⁶⁾ The 4f⁶5d¹ energy level of Eu²⁺ and the transition in the 4f⁷(⁸S_7/2) → 4f⁶(⁷F)5d¹ inorganic host are transformed by the covalent bond and the polarization possibility of the Eu²⁺-ligand interaction.^17-20) The activator ions in the SLA are surrounded by a network of condensed AlN₄ and LiN₄ tetrahedrons. Therefore, the more polarizable circumstance of nitrides provides a stronger nephelauxetic effect than that of, for example, an oxide environment, which results in a greater crystal field splitting and a stronger ionic character to lower the 4f⁶5d¹ excitation state of Eu²⁺. Since the energy difference between the 4f⁷ ground state and the 4f⁶5d¹ excited state is reduced, the absorption and the light-emitting transition shift to the red spectrum region.